{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 多项式回归问题\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.          1.295      -0.00164286]]\n",
      "[ 89.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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JFM5VmM9afkaHGh1suHNj0sAKh/EfMTHO0/b69YMrV+Cdd+DddyFfvhQ3vRp3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\nxqSJnarykHWH11E3rC4vffs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      "text/plain": [
       "<matplotlib.figure.Figure at 0x283a67eec18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure() # 实例化作图变量\n",
    "plt.title('single variable') # 图像标题\n",
    "plt.xlabel('x') # x轴文本\n",
    "plt.ylabel('y') # y轴文本\n",
    "plt.axis([30, 400, 100, 400])\n",
    "plt.grid(True) # 是否绘制网格线\n",
    "\n",
    "x = [[50],[100],[150],[200],[250],[300]]\n",
    "y = [[150],[200],[250],[280],[310],[330]]\n",
    "x_test = [[250],[300]] # 用来做最终效果测试\n",
    "y_test = [[310],[330]] # 用来做最终效果测试\n",
    "plt.plot(x, y, 'k.')\n",
    "\n",
    "model = LinearRegression()\n",
    "model.fit(x, y)\n",
    "x2 = [[30], [400]]\n",
    "y2 = model.predict(x2)\n",
    "plt.plot(x2, y2, 'g-') # 线性回归\n",
    "\n",
    "xx = np.linspace(30, 400, 100) # 设计x轴一系列点作为画图的x点集\n",
    "quadratic_featurizer = PolynomialFeatures(degree=2) # 实例化一个二次多项式特征实例，可以把degree改成3，效果提升不会太多，而且会导致过拟合。\n",
    "x_train_quadratic = quadratic_featurizer.fit_transform(x) # 用二次多项式对样本X值做变换\n",
    "# x被转换为[1, x, x^2]\n",
    "xx_quadratic = quadratic_featurizer.transform(xx.reshape(xx.shape[0], 1)) # 把训练好X值的多项式特征实例应用到一系列点上,形成矩阵\n",
    "regressor_quadratic = LinearRegression() # 创建一个线性回归实例\n",
    "regressor_quadratic.fit(x_train_quadratic, y) # 以多项式变换后的x值为输入，代入线性回归模型做训练\n",
    "plt.plot(xx, regressor_quadratic.predict(xx_quadratic), 'r-') # 用训练好的模型作图\n",
    "print(regressor_quadratic.coef_)\n",
    "print(regressor_quadratic.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07555555555555149"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(x_test, y_test) # 线性模型分数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99933673469387985"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_test_quadratic = quadratic_featurizer.transform(x_test)\n",
    "regressor_quadratic.score(x_test_quadratic, y_test) # 二次多项式回归分数"
   ]
  }
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